We are asked to find the missing sides of the given right-angled triangle.
This is a special right-angled triangle known as the "30°-60°-90°" triangle.
There is a fixed ratio of side lengths in such a triangle.
As you can see, the lengths of sides are
Side opposite of 30° = x
Side opposite of 60° = x√3
Side opposite of 90° = 2x
We are given the side opposite to 60°
So, we can write
[tex]\begin{gathered} x\sqrt[]{3}=11\sqrt[]{3} \\ x=\frac{11\sqrt[]{3}}{\sqrt[]{3}} \\ x=11 \end{gathered}[/tex]
So, the length of the side opposite of 30° is 11
And the length of the side opposite of 90° is
[tex]2x=2(11)=22[/tex]
Therefore, the side lengths of the given triangle are
Side opposite of 30° = x = 11
Side opposite of 60° = x√3 = 11√3
Side opposite of 90° = 2x = 22
